Noncommutative unique factorization domain

Noncommutative unique factorization domain

In mathematics, the noncommutative unique factorization domain is the noncommutative counterpart of the commutative or classical unique factorization domain (UFD).

Example

  • The ring of integral quaternions. If the coefficients a0, a1, a2, a3 are integers or halves of odd integers of a rational quaternion a = a0 + a1i + a2j + a3k then the quaternion is integral.

References

  • "Certain number-theoretic episodes in algebra", R. Sivaramakrishnan; Publisher CRC Press, 2006, ISBN 0824758951

Notes



Wikimedia Foundation. 2010.

Игры ⚽ Нужно сделать НИР?

Look at other dictionaries:

  • Integral domain — In abstract algebra, an integral domain is a commutative ring that has no zero divisors,[1] and which is not the trivial ring {0}. It is usually assumed that commutative rings and integral domains have a multiplicative identity even though this… …   Wikipedia

  • Ring (mathematics) — This article is about algebraic structures. For geometric rings, see Annulus (mathematics). For the set theory concept, see Ring of sets. Polynomials, represented here by curves, form a ring under addition and multiplication. In mathematics, a… …   Wikipedia

  • Polynomial ring — In mathematics, especially in the field of abstract algebra, a polynomial ring is a ring formed from the set of polynomials in one or more variables with coefficients in another ring. Polynomial rings have influenced much of mathematics, from the …   Wikipedia

  • Glossary of ring theory — Ring theory is the branch of mathematics in which rings are studied: that is, structures supporting both an addition and a multiplication operation. This is a glossary of some terms of the subject. Contents 1 Definition of a ring 2 Types of… …   Wikipedia

  • Ring theory — In abstract algebra, ring theory is the study of rings algebraic structures in which addition and multiplication are defined and have similar properties to those familiar from the integers. Ring theory studies the structure of rings, their… …   Wikipedia

  • Emmy Noether — Amalie Emmy Noether Born 23 March 1882(1882 03 23) …   Wikipedia

  • Ascending chain condition on principal ideals — In abstract algebra, the ascending chain condition can be applied to the posets of principal left, principal right, or principal two sided ideals of a ring, partially ordered by inclusion. The ascending ascending chain condition on principal… …   Wikipedia

  • mathematics — /math euh mat iks/, n. 1. (used with a sing. v.) the systematic treatment of magnitude, relationships between figures and forms, and relations between quantities expressed symbolically. 2. (used with a sing. or pl. v.) mathematical procedures,… …   Universalium

  • algebra — /al jeuh breuh/, n. 1. the branch of mathematics that deals with general statements of relations, utilizing letters and other symbols to represent specific sets of numbers, values, vectors, etc., in the description of such relations. 2. any of… …   Universalium

  • algebra, modern — ▪ mathematics Introduction also called  abstract algebra        branch of mathematics concerned with the general algebraic structure of various sets (such as real numbers (real number), complex numbers (complex number), matrices (matrix), and… …   Universalium

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”